electric bikes can be really good but it depends on their purpose. They are really great for old or infirm people, or for people who cycle with a heavy trailer or other heavy loads, or if you have really steep hills or strong headwind or just want to arrive at work half as sweaty as otherwise.
An electric bike will not, however, save you a whole lot of money, compared to public transport or even cars (if several people take the same car); this is due to the fairly hefty price of decent electric bikes, as you mention, but also due to more maintenance than normal bikes, and, especially, due to the price of batteries. I had a Wisper 905SE: lovely bike but the battery only lasted about 7500km and would have cost roughly $1000 to replace. I sold it instead and bought a second-hand good-quality normal bike, for $550. Money-wise, I only broke even with the Wisper, in terms of saved petrol and car insurance. Maintenance was a bit of a headache though, because electric bikes wear down faster than normal bikes, especially the spokes and axle of the wheel(s) bearing the motor(s), and problems were harder to fix than with normal bikes, and most bicycle repairmen refused to look at the bike, not being used to electric bikes and worrying about making mistakes (even when just replacing a spoke, for instance).
The biggest benefit of my Wisper was that it trained me up to cycle to work and back, 53km roundtrip = 2x16 miles, and it helped get me back into shape. By the time I sold it, it was not hard to ride that distance on the (decent but not fancy) bikes that I now use, a MTX and a road bike, depending on the weather and how rough the road on my trip will be. It took a few months, half a year at most, before my body got completely used to the trip. I am now in ok shape (lost almost 30lbs since before the electric bike) and am actually saving a fair bit of money each week (~$45 in saved petrol alone). I am even saving time since going by car would actually take longer (each way by bike takes about 50-55min), due to morning and evening congestion, and lack of parking spaces close to work, and no longer stress about being late for work due to traffic accidents or similar delays.
I cycle 3-5 times to work and back each week (depending on teaching schedules), here in car-dominated Sydney, and also cycle to indoor climbing once a week (adding either 16km = 10miles or 66km = 41miles, depending on work schedule), and also ride to local shops and go on a big weekly shopping 6.5km = 4miles away, filling up my big backpack), and also use the bike when visiting friends or going into town or to the beach, say, (both 25km = 15.5miles) away. All in all, taking the (non-electric) bike is now just a natural thing to do, just like it once seemed natural to take the motorbike (now sold) or the car (hardly used any more). Rather than feel tired, all this bike riding seems to give me a lot of energy, and I get to work feeling happy and almost bouncy :)
So, to answer your question more concisely, I am fairly sure that your particular travel distances and activities would comfortably allow travel by (normal) bike. This would be less bother, and cheaper, than an electric bike, and would, once you have gotten used to it, give you energy rather than drain you. You could use an electric bike as a transitional device, as I ended up doing, but this might be more bother than necessary.
One bit of important advice, whether you get an electric bike or a normal bike: don't cut corners but buy quality (and good batteries if electric). With those distances, prioritise reliability over speed, so as to avoid punctures and repairs. For instance, the fat and not-super-speedy tires on my MTX (Continental's Town and Country) have so far lasted 6000km = 3700miles and should last about half that again - and have never been punctured by anything less than nails.
Anyway, a long-winded and rambling answer - but hopefully of some use!
PS: I would not get a scooter :)